Title: Spin representations of maximal compact subgroups/subalgebras of real
Kac-Moody groups/algebras
Abstract: String theorists are interested in the maximal compact
subgroup/subalgebra of the split real Kac-Moody group/algebra of type
E10. Damour et al. and Nicolai et al. described a spin representation
of this Lie algebra as an extension of the classical spin
representation of the so(10) embedded along the A9 subdiagram.
In my talk I will discuss how to construct such a spin representation
for arbitrary simply laced type. The quotients thus obtained will
always be compact and even perfect if the diagram does not admit any
isolated nodes.
Furthermore I will show how to lift this representation to group level
via amalgamation methods. Along the way we will construct a double
spin cover of the maximal compact subgroup of the simply laced real
Kac-Moody group whose existence has been conjectured by string
theorists.
Moreover, using covering theory of compact Lie groups, this in turn
will allow us to construct spin covers for arbitary two-spherical real
Kac-Moody groups.
The observations on algebra level are joint with G. Hainke and P.
Levy, those on group level joint with D. Ghatei, M. Horn and S. Weiss.